A reparable multistate device with arbitrarily distributed repair times

Chung, Who Keé

doi:10.1016/0026-2714(81)90398-x

Cited by 16 publications

(7 citation statements)

References 3 publications

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“…In recent years, mathematical models governed by distributed parameter systems of coupled partial and ordinary hybrid equations have been widely used to study the reliability of reparable systems (cf. [3,6,8,9,10,11,12,23]). Reliability is defined as the probability that the system, subsystem or component will operate successfully by a given time t (cf.…”

Section: Introductionmentioning

confidence: 99%

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

Hu,

Lai,

et al. 2017

Preprint

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We discuss the problem of optimal impulse control representing the preventive maintenance of a simple reparable system. The system model is governed by coupled transport and integro-differential equations in a nonreflexive Banach space. The objective of this paper is to construct nonnegative impulse control inputs at given system running times that minimize the probability of the system in failure mode. To guarantee the nonnegativity of the controlled system, we consider the control inputs to depend on the system state. This essentially leads to a bilinear control problem. We first present a rigorous proof of existence of an optimal controller and then apply the variational inequality to derive the first-order necessary conditions of optimality.

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Section: Introductionmentioning

confidence: 99%

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

Hu,

Lai,

et al. 2017

Preprint

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“…Chung [1] developed the mathematical model of the device with arbitrarily distributed repair time by supplementary variable technique and discussed the steady-state solution. However, when the repair rate is time-dependent, the well-posedness and asymptotic stability of this system need to be proved strictly.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we are dedicated to discussing the exponential stability of this device, which is significant for the robustness of the system. differential equations according to [1]:…”

Section: Introductionmentioning

confidence: 99%

Exponential Stability of a Reparable Multi-State Device

et al. 2007

Jrl Syst Sci & Complex

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The exponential stability of a multi-state device is discussed in this paper. We present that the C0-semigroup generated by the system operator is quasi-compact and irreducible. It is known that 0 is a simple eigenvalue of the system operator. In combination with this, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfuction corresponding to the simple eigenvalue 0.

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“…By the method of probability analysis, the mathematical model associated with Figure 1 can be expressed as (see [7]) dp…”

Section: Device Formulationmentioning

confidence: 99%

“…But in many practical cases, the repair time of a failed device is arbitrarily distributed. Chung [7] extended the work of Elsayed and Zebib [6] and developed a mathematical model of the device with arbitrarily distributed repair time. Further, Chung [7] derived steady availability of the device by the method of inversion of the Laplace transform.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic property of a reparable multi-state device

Zhu

2005

Quart. Appl. Math.

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Abstract. This paper is devoted to studying the existence, uniqueness and asymptotic stability of a multi-state device's time-dependent solution. C 0 semigroup theory is used to prove the existence of a unique non-negative solution of the device. Moveover, by analyzing the spectrum of the system operator generated by the device, this paper proves that 0 is the unique spectral point on the imaginary axis and the other spectra lie in the left half plane. As a result, the asymptotic behavior of a multi-state device is obtained.

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A reparable multistate device with arbitrarily distributed repair times

Cited by 16 publications

References 3 publications

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

Optimal Impulse Control of a Simple Reparable System in a Nonreflexive Banach Space

Exponential Stability of a Reparable Multi-State Device

Asymptotic property of a reparable multi-state device

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